The present invention relates to a planning system and a planning method, and more particularly to technology for offering meshing information when an assigned section is to be taken charge of by a plurality of persons in distributing and collecting items and discussing various problems, technology for offering meshing information for conducting strength test of an article, technology for offering work division information when a work is to be conducted by a plurality of persons or technology for offering meshing information technology for conducting city planning, and further particularly to linear programming system and method suitable for determining a solution with a simple construction as to a problem for unifying the meshing.
The meshing planning and designing relates to a problem to divide a given assigned section (one to three-dimension) by a given divisor and determine such a solution that makes weights of the divided sections, for example, areas, weights or work amounts uniform for each divided section.
This problem is considered as a kind of clustering problem. Namely, it is equivalent to "determine a direct sum partition {S.sub.1, . . . , S.sub.n } (where S.sub.i is a set of divisions) of a definite set of patterns W which minimizes summation of distortion (S.sub.1, . . . , S.sub.n) (where S.sub.i is a set of divisions) for such W".
There are only a definite number of methods for direct sum partitioning the definite set W having M elements into N partial sets and hence it has been known that this problem can necessarily be solved by an enumeration method in principle but the number of cases (the number of combinations) of such direct sum partition is: ##EQU1##
Accordingly, in an actual problem, for example, in case of M&gt;1,000 and N&gt;100, it is a huge number and it is very difficult to get a solution within a practical time even if a today's fastest computer is used.
For this problem, an LBG algorithm as disclosed in the article "Algorithm for Pattern Recognition and Learning", Bunnichi Sohgoh Shuppan, by Y. Kamisaka and K. Ozaki, p. 112.about.119 or various OR (operations research method) techniques have been proposed.
However, the planning method disclosed in the above reference includes at least two problems.
First, in order to determine an optimum meshing plan, a repetitive process of at least third power of the number N of elements of a problem in question is needed and it is very difficult to determine a solution at a high speed.
Secondly, there is a problem of very low probability of reaching an optimum solution.